Syrian President Hafez Assad's decision to close the Damascus offices of the Arab world's leading terrorist was "the major act" leading to the Reagan administration's decision to send a high-level envoy there to discuss an improvement in U.S.-Syrian relations, U.S. officials said yesterday.

Assad has sent a "generally positive" reply to President Reagan's recent letter indicating a renewed U.S. interest to explore "the possibilities of a dialogue" with Syria "on a number of issues" and an offer to send an emissary, White House spokesman Marlin Fitzwater said yesterday.

The issues include the Middle East peace process and the status of the nine Americans being held hostage by Shiite extremists in Lebanon, where Syria has "assumed a major role," Fitzwater said.

Relations between the United States and Syria worsened last November when the administration imposed economic sanctions and ordered all American oil companies to leave that country following the conviction in a British court of Nazir Hindawi, who implicated Syrian intelligence in his attempted bombing of an El Al airliner at London's Heathrow Airport in April 1986.

The administration also barred all visits by high-level U.S. officials to Damascus. The month before, it had recalled the U.S. ambassador to Syria, William L. Eagleton Jr., in protest over the incident.

Fitzwater refused yesterday to say whom the White House plans to send to Damascus or when the envoy might leave, but he hinted that the U.S. ambassador to the United Nations, Vernon A. Walters, could be the choice.

He said the administration's decision to send an envoy does not mean it is about to send Eagleton back to Damascus or signal a change in U.S. policy toward the Assad regime. But he said it was "probably fair to say that there would be some general improvement in diplomatic relations just by virtue of establishing a dialogue."

U.S. officials said yesterday that the administration concluded only recently that Assad has finally shut down the offices of Sabri Banna, better known as Abu Nidal, whom it has described as the leader of "the most active and brutal international terrorist group operating today."

The location of Abu Nidal's offices only a few blocks from the U.S. Embassy in Damascus had particularly irked the administration and become a major source of its suspicions that Assad, despite his claims to the contrary, was still sponsoring state terrorism.

The administration had been awaiting some gesture from Assad to indicate that he was distancing himself from terrorist activities before moving to improve relations with his regime, and the closing of Abu Nidal's offices was "the major act" it was looking for, one U.S. official said.

Both the closing of his offices and evidence that Assad has removed or demoted his former Air Force chief of intelligence, Maj. Gen. Mohammed Khuli, as his chief security adviser have been taken by U.S. officials as positive signs that the Syrian president is taking steps to end his government's involvement in terrorism, at least temporarily.

The Syrian intelligence officer, a longtime close collaborator of Assad, was implicated in the London El Al bombing attempt, although the Syrian government repeatedly denied the allegations.

Reagan's decision to send an envoy leaves the administration's relations with the Assad government in flux. After a lengthy internal debate in early May, the administration decided against sending Eagleton back to Damascus before Assad gave some concrete indication that he was distancing himself from terrorism.

Reports that Assad had closed Abu Nidal's offices began to surface in the Jordanian press early this month. But U.S. antiterrorist specialists were not immediately convinced by the reports, and only "a week or so ago" did they finally conclude that the offices were closed, according to one administration source.

They are not sure that Abu Nidal's camps in the Syrian-controlled Bekaa Valley of eastern Lebanon have been shut or that representatives of his Fatah Revolutionary Council have been thrown out of the country as the Jordan Times reported June 4.